Question

В потоке 65 человек. Из них 26 играют в баскетбол, 33 - в хоккей и столько же в волейбол. Увлекаются двумя видами спорта - баскетболом и хоккеем - 8, баскетболом и волейболом - 11, волейболом и хоккеем - 13. Двое не увлекаются ни баскетболом, ни хоккеем, ни волейболом. Сколько ребят одновременно увлекаются всеми видами спорта?

Answer 1

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Answer 2

Problem Analysis

We are given the following information about a group of 65 people: - 26 people play basketball. - 33 people play hockey. - 33 people play volleyball. - 8 people play both basketball and hockey. - 11 people play both basketball and volleyball. - 13 people play both volleyball and hockey. - 2 people do not play any of the three sports.

We need to determine how many people play all three sports simultaneously.

Solution

To solve this problem, we can use the principle of inclusion-exclusion. We will start by counting the number of people who play at least one sport and then subtract the number of people who play only one or two sports.

Let's calculate the number of people who play at least one sport:

- Number of people who play basketball: 26 - Number of people who play hockey: 33 - Number of people who play volleyball: 33

To find the total number of people who play at least one sport, we can add these numbers together:

26 + 33 + 33 = 92

However, we have counted some people multiple times because they play more than one sport. To correct this, we need to subtract the number of people who play only one sport.

- Number of people who play only basketball: 26 - (8 + 11) = 7 - Number of people who play only hockey: 33 - (8 + 13) = 12 - Number of people who play only volleyball: 33 - (11 + 13) = 9

Now, let's subtract these numbers from the total number of people who play at least one sport:

92 - (7 + 12 + 9) = 64

So, there are 64 people who play at least one sport.

Finally, we need to subtract the number of people who do not play any of the three sports:

64 - 2 = 62

Therefore, 62 people simultaneously play all three sports.

Answer

There are 62 people who simultaneously play basketball, hockey, and volleyball.